Results for 'A. Lindenbaum'

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  1.  42
    Über die Beschränktheit der Ausdrucksmittel deduktiver Theorien.A. Lindenbaum & A. Tarski - 1936 - Journal of Symbolic Logic 1 (3):115-116.
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  2.  46
    Actualités de la personne en Mélanésie.Shirley Lindenbaum - 2008 - Cahiers Internationaux de Sociologie 124 (1):83.
    Les anthropologues qui étudient les effets de la « modernité » en Mélanésie ont donné un souffle nouveau à la question de la personne relationnelle. On observe l’apparition de personnes plus individualisées, plus autonomes dans le contexte de la conversion au christianisme, de la consommation de biens et du travail salarié. Comportements sexuels et sensibilités des jeunes se transforment à la faveur de leur expérience d’idées nouvelles sur les rapports amoureux et de formes inédites d’érotisme, bien que toujours soumis à (...)
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  3.  17
    Different Patterns of Attention Modulation in Early N140 and Late P300 sERPs Following Ipsilateral vs. Contralateral Stimulation at the Fingers and Cheeks. [REVIEW]Laura Lindenbaum, Sebastian Zehe, Jan Anlauff, Thomas Hermann & Johanna Maria Kissler - 2021 - Frontiers in Human Neuroscience 15.
    Intra-hemispheric interference has been often observed when body parts with neighboring representations within the same hemisphere are stimulated. However, patterns of interference in early and late somatosensory processing stages due to the stimulation of different body parts have not been explored. Here, we explore functional similarities and differences between attention modulation of the somatosensory N140 and P300 elicited at the fingers vs. cheeks. In an active oddball paradigm, 22 participants received vibrotactile intensity deviant stimulation either ipsilateral or contralateral at the (...)
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  4.  47
    (2 other versions)A sufficient and necessary condition for Tarski's property in lindenbaum's extensions.Teodor Stepień - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (26‐29):447-453.
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  5.  15
    (1 other version)A generalization of lindenbaum's theorem for predicate calculi.Konrad Schultz - 1984 - Mathematical Logic Quarterly 30 (9‐11):165-168.
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  6.  32
    Hosiasson-lindenbaum/kolmogorov probability theory: Solutions to exercises in appendix a of extended version of “modus ponens and modus tollens …”.Jordan Howard Sobel - manuscript
  7.  52
    Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References.Jan Zygmunt & Robert Purdy - 2014 - Logica Universalis 8 (3-4):285-320.
    Notes on the life of Adolf Lindenbaum, a complete bibliography of his published works, and selected references to his unpublished results.
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  8. Lindenbaum, Adolf.Jan Woleński - 2015 - Internet Encyclopedia of Philosophy.
    Adolf Lindenbaum Adolf Lindenbaum was a Polish mathematician and logician who worked in topology, set theory, metalogic, general metamathematics and the foundations of mathematics. He represented an attitude typical of the Polish Mathematical School, consisting of using all admissible methods, independently of whether they were finitary. For example, the axiom of choice was freely applied, … Continue reading Lindenbaum, Adolf →.
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  9.  27
    Lindenbaum-Type Logical Structures.Sayantan Roy, Sankha S. Basu & Mihir K. Chakraborty - 2023 - Logica Universalis 17 (1):69-102.
    In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a (...)-type, show their separations, and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski–Lindenbaum-type logical structures. (shrink)
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  10.  34
    Lindenbaum algebras of intuitionistic theories and free categories.Peter Freyd, Harvey Friedman & Andre Scedrov - 1987 - Annals of Pure and Applied Logic 35 (C):167-172.
    We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on (...)
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  11. The relation of a to $\operatorname{prov} \ulcorner a \urcorner$ in the lindenbaum sentence algebra.C. F. Kent - 1973 - Journal of Symbolic Logic 38 (2):295 - 298.
  12.  53
    The lindenbaum algebra of the theory of the class of all finite models.Steffen Lempp, Mikhail Peretyat'kin & Reed Solomon - 2002 - Journal of Mathematical Logic 2 (02):145-225.
    In this paper, we investigate the Lindenbaum algebra ℒ of the theory T fin = Th of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra /ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These (...)
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  13.  21
    Tiny models of categorical theories.M. C. Laskowski, A. Pillay & P. Rothmaler - 1992 - Archive for Mathematical Logic 31 (6):385-396.
    We explore the existence and the size of infinite models of categorical theories having cardinality less than the size of the associated Tarski-Lindenbaum algebra. Restricting to totally transcendental, categorical theories we show that “Every tiny model is countable” is independent of ZFC. IfT is trivial there is at most one tiny model, which must be the algebraic closure of the empty set. We give a new proof that there are no tiny models ifT is not totally transcendental and is (...)
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  14.  32
    Janina Hosiasson-Lindenbaum on Analogical Reasoning: New Sources.Marta Sznajder - 2024 - Erkenntnis 89 (4):1349-1365.
    Janina Hosiasson-Lindenbaum is a known figure in philosophy of probability of the 1930s. A previously unpublished manuscript fills in the blanks in the full picture of her work on inductive reasoning by analogy, until now only accessible through a single publication. In this paper, I present Hosiasson’s work on analogical reasoning, bringing together her early publications that were never translated from Polish, and the recently discovered unpublished work. I then show how her late work relates to Rudolf Carnap’s approach (...)
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  15.  8
    The higher dimensional propositional calculus.A. Bucciarelli, P.-L. Curien, A. Ledda, F. Paoli & A. Salibra - forthcoming - Logic Journal of the IGPL.
    In recent research, some of the present authors introduced the concept of an $n$-dimensional Boolean algebra and its corresponding propositional logic $n\textrm{CL}$, generalizing the Boolean propositional calculus to $n\geq 2$ perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for $n\textrm{CL}$, named $n\textrm{LK}$. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that $n\textrm{LK}$ enjoys the cut admissibility property. The latter relies on the generalization to the $n$-ary case (...)
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  16.  92
    Some restricted lindenbaum theorems equivalent to the axiom of choice.David W. Miller - 2007 - Logica Universalis 1 (1):183-199.
    . Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional . A (...)
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  17.  48
    Functors of Lindenbaum-Tarski, Schematic Interpretations, and Adjoint Cylinders between Sentential Logics.J. Climent Vidal & J. Soliveres Tur - 2008 - Notre Dame Journal of Formal Logic 49 (2):185-202.
    We prove, by using the concept of schematic interpretation, that the natural embedding from the category ISL, of intuitionistic sentential pretheories and i-congruence classes of morphisms, to the category CSL, of classical sentential pretheories and c-congruence classes of morphisms, has a left adjoint, which is related to the double negation interpretation of Gödel-Gentzen, and a right adjoint, which is related to the Law of Excluded Middle. Moreover, we prove that from the left to the right adjoint there is a pointwise (...)
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  18.  43
    Direct Proofs of Lindenbaum Conditionals.René Gazzari - 2014 - Logica Universalis 8 (3-4):321-343.
    We discuss the problem raised by Miller to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of Choice is not applied.
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  19.  39
    Quantum logics and lindenbaum property.Roberto Giuntini - 1987 - Studia Logica 46 (1):17 - 35.
    This paper will take into account the Lindenbaum property in Orthomodular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibility of extending any semantically non-contradictory set of formulas to a semantically non-contradictory complete set of formulas. The main purpose of this paper is to show that (...)
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  20.  4
    The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $$\omega $$-stable theories.Mikhail Peretyat’kin - forthcoming - Archive for Mathematical Logic:1-12.
    We study the class of all strongly constructivizable models having \(\omega \) -stable theories in a fixed finite rich signature. It is proved that the Tarski–Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean \(\Sigma ^1_1\) -algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of all Boolean \(\Sigma ^1_1\) -algebras. This gives a characterization to the (...)
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  21.  16
    (2 other versions)On Number of Lindenbaum's Oversystems of Propositional and Predicate Calculi.Teodor Stepień - 1985 - Mathematical Logic Quarterly 31 (21‐23):333-344.
    The present paper is a continuation of [6] and [7]. Thus the content of this paper is the following. At first we establish properties of systems S 2 n and S 2∗ n , where systems S 2 n and S 2∗ n are extensions of Rasiowa-S lupecki’s systems Sn and S ∗ n . Then we shall show that for every cardinal number m there exist a system ST 4 m of propositional calculus and a system SP 4 m (...)
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  22.  71
    Remarks on the Scott–Lindenbaum Theorem.Gillman Payette & Peter K. Schotch - 2014 - Studia Logica 102 (5):1003-1020.
    In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously prosecuted (...)
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  23.  27
    Uniform Density in Lindenbaum Algebras.V. Yu Shavrukov & Albert Visser - 2014 - Notre Dame Journal of Formal Logic 55 (4):569-582.
    In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we prove a (...)
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  24.  23
    Craig-godel-lindenbaum's property and sobocinski-tarski's property in propositional calculi.Teodor Stepien - 1981 - Bulletin of the Section of Logic 10 (3):116-120.
    In the paper we give a sucient condition of the Interpolation Property in propositional calculi; then we establish the power of the class of the systems with Craig's property. Next we show that there does not exist a minimal R0-system with Craig-Godel-Lindenbaum's property. Finally, we generalize Sobocinski-Tarskis theorem concerning Sobocinski-Tarski's property.
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  25.  29
    Lindenbaumologia I: A teoria geral.Edélcio de Souza - 2001 - Cognitio 2:213-219.
    Resumo: Apresentamos uma abordagem geral da demonstração de completude de cálculos lógicos abstratos por meio da noção de valoração e de um resultado devido a A. Lindenbaum.: We present a general approach to the proof the completeness of abstract logical calculi through the notion of valuation and of a result due to A. Lindenbaum.
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  26.  43
    A theorem of the degree of complexity of some sentential logics.Jacek Hawranek & Jan Zygmunt - 1980 - Bulletin of the Section of Logic 9 (2):67-69.
    x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.
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  27.  26
    The Jacobson Radical of a Propositional Theory.Giulio Fellin, Peter Schuster & Daniel Wessel - 2022 - Bulletin of Symbolic Logic 28 (2):163-181.
    Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum’s Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko’s Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style (...)
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  28.  38
    A proof of axiomatizability of łukasiewicz’s three-valued implicational propositional calculus.T. Prucnal - 1967 - Studia Logica 20 (1):144-144.
    LetL 3 c be the smallest set of propositional formulas, which containsCpCqpCCCpqCrqCCqpCrpCCCpqCCqrqCCCpqppand is closed with respect to substitution and detachment. Let $\mathfrak{M}_3^c $ be Łukasiewicz’s three-valued implicational matrix defined as follows:cxy=min (1,1−x+y), where $x,y \in \{ 0,\tfrac{1}{2},1\}$ . In this paper the following theorem is proved: $$L_3^c = E( \mathfrak{M}_3^c )$$ The idea used in the proof is derived from Asser’s proof of completeness of the two-valued propositional calculus. The proof given here is based on the Pogorzelski’s deduction theorem fork-valued (...)
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  29.  19
    Fibred algebraic semantics for a variety of non-classical first-order logics and topological logical translation.Yoshihiro Maruyama - 2021 - Journal of Symbolic Logic 86 (3):1189-1213.
    Lawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics. This yields uniform hyperdoctrinal completeness results for numerous logics such as different types of relevant predicate logics and beyond, which are new results on their own; i.e., we give uniform categorical semantics for a broad variety of non-classical predicate logics. And (...)
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  30.  78
    Abacus logic: The lattice of quantum propositions as the poset of a theory.Othman Qasim Malhas - 1994 - Journal of Symbolic Logic 59 (2):501-515.
    With a certain graphic interpretation in mind, we say that a function whose value at every point in its domain is a nonempty set of real numbers is an Abacus. It is shown that to every collection C of abaci there corresponds a logic, called an abacus logic, i.e., a certain set of propositions partially ordered by generalized implication. It is also shown that to every collection C of abaci there corresponds a theory JC in a classical propositional calculus such (...)
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  31.  58
    Implicational (semilinear) logics I: a new hierarchy. [REVIEW]Petr Cintula & Carles Noguera - 2010 - Archive for Mathematical Logic 49 (4):417-446.
    In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding (...)
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  32. Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.) - 2005 - Boston: Birkhäuser Verlog.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the (...)
  33. On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Springer. pp. 284-298.
    In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...)
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  34.  70
    De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics.Paul Égré, Lorenzo Rossi & Jan Sprenger - 2021 - Journal of Philosophical Logic 50 (2):215-247.
    In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for (...)
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  35.  60
    Hereditarily Structurally Complete Superintuitionistic Deductive Systems.Alex Citkin - 2018 - Studia Logica 106 (4):827-856.
    Propositional logic is understood as a set of theorems defined by a deductive system: a set of axioms and a set of rules. Superintuitionistic logic is a logic extending intuitionistic propositional logic \. A rule is admissible for a logic if any substitution that makes each premise a theorem, makes the conclusion a theorem too. A deductive system \ is structurally complete if any rule admissible for the logic defined by \ is derivable in \. It is known that any (...)
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  36. W duchu Tarskiego: o alternatywach teorio-dowodowej metalogiki.Stanisław J. Surma - 1993 - Filozofia Nauki 1.
    the standard metalogical set-ups seem to be all based on the idea of consequence (or proof). However, metalogic can also be effectively constructed using some non-standard primmitive ideas. In this paper an outline is given to four metalogical frameworks, alternative to the standard set-ups. They are based, respectively, on the idea of consistency; on an omission (or separation) operator; on an extension operator (called in the paper a Lindenbaum operator); and on the idea of maximality. All these metalogics, including (...)
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  37.  44
    Level Compactness.Gillman Payette & Blaine D'Entremont - 2006 - Notre Dame Journal of Formal Logic 47 (4):545-555.
    The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts which appear in d'Entremont's master's thesis, "Inference and Level." We will (...)
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  38.  28
    Some Boolean Algebras with Finitely Many Distinguished Ideals I.Regina Aragón - 1995 - Mathematical Logic Quarterly 41 (4):485-504.
    We consider the theory Thprin of Boolean algebras with a principal ideal, the theory Thmax of Boolean algebras with a maximal ideal, the theory Thac of atomic Boolean algebras with an ideal where the supremum of the ideal exists, and the theory Thsa of atomless Boolean algebras with an ideal where the supremum of the ideal exists. First, we find elementary invariants for Thprin and Thsa. If T is a theory in a first order language and α is a linear (...)
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  39.  62
    Paraconsistent algebras.Walter Alexandre Carnielli & Luiz Paulo Alcantara - 1984 - Studia Logica 43 (1-2):79 - 88.
    The prepositional calculiC n , 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum''s algebra forC n . C. Mortensen settled the problem, proving that no equivalence relation forC n . determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC n , as well as the concept of paraconsistent closure (...)
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  40. Swap structures semantics for Ivlev-like modal logics.Marcelo E. Coniglio & Ana Claudia Golzio - 2019 - Soft Computing 23 (7):2243-2254.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...)
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  41. Undecidability in diagonalizable algebras.V. Shavrukov - 1997 - Journal of Symbolic Logic 62 (1):79-116.
    If a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.
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  42.  24
    Amalgamation and Robinson property in universal algebraic logic.Zalán Gyenis & Övge Öztürk - forthcoming - Logic Journal of the IGPL.
    There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also shown that given (...)
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  43.  23
    Interpretation of De Finetti coherence criterion in Łukasiewicz logic.Daniele Mundici - 2010 - Annals of Pure and Applied Logic 161 (2):235-245.
    De Finetti gave a natural definition of “coherent probability assessment” β:E→[0,1] of a set E={X1,…,Xm} of “events” occurring in an arbitrary set of “possible worlds”. In the particular case of yes–no events, , Kolmogorov axioms can be derived from his criterion. While De Finetti’s approach to probability was logic-free, we construct a theory Θ in infinite-valued Łukasiewicz propositional logic, and show: a possible world of is a valuation satisfying Θ, β is coherent iff it is a convex combination of valuations (...)
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  44. The Quantified Argument Calculus with Two- and Three-valued Truth-valuational Semantics.Hongkai Yin & Hanoch Ben-Yami - 2022 - Studia Logica 111 (2):281-320.
    We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true (...)
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  45.  33
    Natural dualities for varieties of BL-algebras.Antonio Di Nola & Philippe Niederkorn - 2005 - Archive for Mathematical Logic 44 (8):995-1007.
    BL-algebras are the Lindenbaum algebras for Hájek's Basic Logic, just as Boolean algebras correspond to the classical propositional calculus. The finite totally ordered BL-algebras are ordinal sums of MV-chains. We develop a natural duality, in the sense of Davey and Werner, for each subvariety generated by a finite BL-chain, and we use it to describe the injective and the weak injective members of these classes.
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  46.  80
    Merging Inference and Conjecture by Information.Cornelia Burger Isabella & Heidema Johannes - 2002 - Synthese 131 (2):223 - 258.
    The intuitive notion of a binary relation on information-bearers, comparingthem with respect to their closeness to the available information, is oftenconstrued in terms of comparing their symmetric difference with, orcompositional similarity to, the available information. This happens forinstance in some treatments of verisimilitude. We expound an abstractmathematical rendering of the relevant data-dependent relation in theframework of Boolean algebras. For every element t of a Boolean algebra B we construct the t-modulated Boolean algebra Btin which the order relation represents `is at (...)
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  47.  62
    Subsystems of second-order arithmetic between RCA0 and WKL0.Carl Mummert - 2008 - Archive for Mathematical Logic 47 (3):205-210.
    We study the Lindenbaum algebra ${\fancyscript{A}}$ (WKL o, RCA o) of sentences in the language of second-order arithmetic that imply RCA o and are provable from WKL o. We explore the relationship between ${\Sigma^1_1}$ sentences in ${\fancyscript{A}}$ (WKL o, RCA o) and ${\Pi^0_1}$ classes of subsets of ω. By applying a result of Binns and Simpson (Arch. Math. Logic 43(3), 399–414, 2004) about ${\Pi^0_1}$ classes, we give a specific embedding of the free distributive lattice with countably many generators into (...)
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  48.  43
    Boolean deductive systems of BL-algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
    BL-algebras rise as Lindenbaum algebras from many valued logic introduced by Hájek [2]. In this paper Boolean ds and implicative ds of BL-algebras are defined and studied. The following is proved to be equivalent: (i) a ds D is implicative, (ii) D is Boolean, (iii) L/D is a Boolean algebra. Moreover, a BL-algebra L contains a proper Boolean ds iff L is bipartite. Local BL-algebras, too, are characterized. These results generalize some theorems presented in [4], [5], [6] for MV-algebras (...)
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  49.  57
    Provability algebras and proof-theoretic ordinals, I.Lev D. Beklemishev - 2004 - Annals of Pure and Applied Logic 128 (1-3):103-123.
    We suggest an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture proof-theoretic information. We use this method to analyze Peano arithmetic and show how an ordinal notation system up to 0 can be recovered from the corresponding algebra in a canonical way. This method also establishes links between proof-theoretic ordinal analysis and the work which has (...)
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  50. Two's Company: The humbug of many logical values.Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos - 2005 - In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. pp. 169-189.
    The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with (...)
     
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